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An experimental study of the brittle-ductile transition
of basalt at oceanic crust pressure and temperature
conditions
Marie Violay, Benoit Gibert, David Mainprice, Brian Evans, Jean-Marie
Dautria, Pierre Azais, Philippe Pezard
To cite this version:
Marie Violay, Benoit Gibert, David Mainprice, Brian Evans, Jean-Marie Dautria, et al.. An
exper-imental study of the brittle-ductile transition of basalt at oceanic crust pressure and temperature
conditions. Journal of Geophysical Research, American Geophysical Union, 2012, 117, pp.B03213.
�10.1029/2011JB008884�. �hal-00760905�
An experimental study of the brittle-ductile transition of basalt
at oceanic crust pressure and temperature conditions
Marie Violay,
1,2Benoit Gibert,
1David Mainprice,
1Brian Evans,
3Jean-Marie Dautria,
1Pierre Azais,
1and Philippe Pezard
1Received 21 September 2011; revised 10 January 2012; accepted 1 February 2012; published 23 March 2012.
[1]
The brittle to ductile transition (BDT) in rocks may strongly influence their transport
properties (i.e., permeability, porosity topology
…) and the maximum depth and
temperature where hydrothermal fluids may circulate. To examine this transition in the
context of Icelandic crust, we conducted deformation experiments on a glassy basalt
(GB) and a glass-free basalt (GFB) under oceanic crust conditions. Mechanical and
micro-structural observations at a constant strain rate of 10
5s
1and at confining pressure
of 100
–300 MPa indicate that the rocks are brittle and dilatant up to 700–800
C. At higher
temperatures and effective pressures the deformation mode becomes macroscopically
ductile, i.e., deformation is distributed throughout the sample and no localized shear
rupture plane develops. The presence of glass is a key component reducing the sample
strength and lowering the pressure of the BDT. In the brittle field, strength is consistent
with a Mohr-Coulomb failure criterion with an internal coefficient of friction of 0.42 for
both samples. In the ductile field, strength is strain rate- and temperature-dependent and
both samples were characterized by the same stress exponent in the range 3 < n < 4.2 but by
very different activation energy Q
GB= 59
15 KJ/mol and Q
GFB= 456
4 KJ/mol.
Extrapolation of these results to the Iceland oceanic crust conditions predicts a BDT at
100
C for a glassy basalt, whereas the BDT might occur in non-glassy basalts at deeper
conditions, i.e., temperatures higher than 550
100
C, in agreement with the Icelandic
seismogenic zone.
Citation: Violay, M., B. Gibert, D. Mainprice, B. Evans, J.-M. Dautria, P. Azais, and P. Pezard (2012), An experimental study of the brittle-ductile transition of basalt at oceanic crust pressure and temperature conditions, J. Geophys. Res., 117, B03213, doi:10.1029/2011JB008884.
1.
Introduction
[2] The mid-ocean ridge system is the largest continuous volcanic feature on Earth, with significant interactions between tectonic activity, volcanism and seawater circula-tion [Macdonald, 1982]. At mid-ocean ridges, new crust is formed and cools by heat conduction and by hydrothermal circulation [e.g., Johnson et al., 1993; Phipps Morgan and Chen, 1993; Stein and Stein, 1994]. Seawater penetrates into the upper crust, and is heated as it moves down toward the base of the sheeted dike complex, in the vicinity of the magma chamber [e.g., Teagle et al., 1998]. The discharge of hydrothermal fluids occurs along the ridge axis at tempera-tures up to400C [e.g., Koschinsky et al., 2008]. At sea-floor the fluid is replaced by seawater“recharge,” creating a circulation cell. During the circulation, the seawater reacts
with oceanic crustal rocks, leading to important processes such mineral dissolution/precipitation and heat exchanges [e.g., Edmond et al., 1982; Alt et al., 1996]. There are some economic uses of hydrothermal circulation, as for example geothermal power [e.g., Pálmason and Sæmundsson, 1979] and mining ore deposits [Nelson and Giles, 1985; Mills and Elderfield, 1995]. To better understand the dynamics of seawater circulation, a fundamental question to be consid-ered is maximum pressure and temperature at which hydrothermal fluids may penetrate by a cracking front at mid-oceanic ridges in the axial region above the axial magma chamber and off axis [Lister, 1980; Stein and Stein, 1994; Elderfield and Schultz, 1996; Manning et al., 1996; Nicolas et al., 2003]. Seawater circulation within the upper oceanic crust depends on the transport properties of oceanic crustal rocks (permeability, porosity topology…), which is strongly influenced by the deformation mode of the crust, i.e., brittle versus ductile deformation, which vary according to a wide range of pressure and temperature conditions [Lockner and Madden, 1991; Fischer and Paterson, 1992; Morrow and Lockner, 1994, 1997; Morrow et al., 1994; Zhu et al., 2007; De Paola et al., 2009]. Indeed, cracks and fractures control the bulk permeability of oceanic crust,
1
Géosciences Montpellier UMR 5243, CNRS, Université Montpellier 2, Montpellier, France.
2
Now at Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy.
3Department of Earth, Atmospheric, and Planetary Sciences,
Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. Copyright 2012 by the American Geophysical Union.
0148-0227/12/2011JB008884
providing critical pathways for hydrothermal fluids and magma [e.g., Norton and Knapp, 1977; Lowell et al., 1995; Singh et al., 1999; Tolstoy et al., 2008].
[3] A partial answer to this question can consequently be provided by the determination of the pressure and tempera-ture of the brittle to ductile transition in oceanic crust rocks, as this depth is often considered to correspond to a signifi-cant modification of the porosity topology [Hirth et al., 1998; Hirose and Hayman, 2008; Nara et al., 2011].
[4] Our current understanding of mid ocean ridge, has been aided by geophysical observation and rheological modeling. On one hand, heat flux measurements and seismic studies show that (i) hydrothermal circulation up to 700C must be taken into account to explain the cooling of the oceanic crust [Sleep and Rosendahl, 1979; Chen and Morgan, 1990; Phipps Morgan and Chen, 1993; Stein and Stein, 1994; Fontaine et al., 2001, 2008] (ii) the lower limit of the oceanic crust seismogenic zone occurs at about 700C [Ranero et al., 1997; Ágústsson and Flovenz, 2005; Bjornsson, 2008]. On the other hand, the rheological model of oceanic crust is poorly constrained due the limited num-ber of experimental mechanical studies of oceanic crustal rocks (basalts, dolerites, gabbros). This paucity is in part due to the difficulty in locating samples with appropriate microstructures for the laboratory experiments. Most gabbros of the lower oceanic crust have grain sizes (>1 cm) that are too large for studies in conventional deformation machines, and most basalts contain too much glassy com-ponent (>25%) to provide realistic flow laws. In order to constrain the rheological properties of basaltic crust, most experimental work has focused on monocrystals or single-phase aggregates of typical minerals such as plagio-clases [Borg and Heard, 1969, 1970; Marshall and MacLaren, 1977a, 1977b; Tullis and Yund, 1977, 1980, 1987, 1991; Dell’Angelo et al., 1987; Dell’Angelo and Tullis, 1988; Dimanov et al., 1998, 1999, 2000; Rybacki and Dresen, 2004], pyroxene [Avé Lallement, 1978; Kollé and Blacic, 1982, 1983; Kirby and Kronenberg, 1984; Dimanov et al., 2003; Dimanov and Dresen, 2005; Moghadam et al., 2010], and olivine [Goetze and Brace, 1972; Kohlstedt and Goetze, 1974; Weertman and Weertman, 1975; Hirth and Kohlstedt, 1995; Zimmerman and Kohlstedt, 2004]. There are also relatively few studies on deformation mechanisms of polyphasic diabases and gabbros [Kronenberg and Shelton, 1980; Shelton and Tullis, 1981; Caristan, 1982; Shimada et al., 1989; Hacker and Christie, 1992; Mackwell et al., 1998; He et al., 2007] and polyphasic synthetic gabbros [Dimanov and Dresen, 2005; Dimanov et al., 2007, 2011]. These studies were performed at very high temperatures and pressures, far from the in situ oceanic crust conditions. Hacker and Christie [1992] pro-vide data at very high pressure (>1 GPa) on basalts under brittle and ductile conditions, but at temperatures where the glassy component dominate the deformation process. Deformation experiments on Maryland diabase by Mackwell et al. [1998] and Caristan [1982] provide some rheological information, but only at high temperature (>900C).
[5] In this paper, we present new data on rheological properties of basalt at oceanic in situ crustal P,T conditions i.e., at confining pressure from 100 to 300 MPa, tempera-ture from 400C to 950C, and pore fluid pressure from 0 to 50 MPa. Two samples were selected for their low porosity
(<3%), their variation in glassy component (glassy basalt/ glass free basalt) and their low degree of alteration. Both samples are representative of a thick basaltic crust formed by a successive stacking of partly glassy volcanic lava flows as Iceland, or Hawaii crust [Kaban et al., 2002; Moore et al., 1982]. Glassy basalt are also common in oceanic crust as showed at ODP hole 896A located south of the Costa Rica Rift [Fisk et al., 1996].
2.
Methods
2.1. Experimental Methods
[6] Cylindrical samples of 10 mm in diameter and 20 mm in length were jacketed with copper or iron after being dried over 48 h at 70C. These assemblies were then deformed in conventional triaxial experiments conducted in a servo-controlled, gas-medium apparatus from “Paterson instru-ments.” Temperatures ranged from 400C to 950C; confining pressures (Pc) from 100 MPa to 300 MPa, and
pore pressures (Pp) from 0 to 50 MPa. Both water and argon
were used as pore fluids. Deformation experiments were generally performed up to strains of 15% with constant strain rate (_ɛ), where 106s1≤ _ɛ ≤ 104s1. The constant
strain rate portion of the tests was usually followed by stress relaxation to evaluate the strain rate sensitivity of stress, but in some experiments, the imposed deformation rate was changed to a new value. Differential stresses were mea-sured with an accuracy of 2 MPa. To reduce jacket strength, copper was used at low temperatures (400 to 750C), whereas iron jackets were used above that range. Corrections were applied to the measured force using jacket strengths estimated from Frost and Ashby [1982] and from the change in sample dimensions with deformation; displacement mea-surements were corrected for apparatus distortion.
2.2. Analytical Methods
[7] After deformation, samples were impregnated with epoxy and then cut parallel to the cylinder axis, or, if deformation was localized, perpendicular to the shear zone. From each sample, a polished, 30 mm, thin section was prepared and examined in an optical microscope using plane-polarized, cross-polarized and reflected light, and in a scanning electron microscope (SEM). Chemical and crys-tallographic information were collected by EPMA micro-analysis and electron backscattered diffraction (EBSD) in SEM.
[8] Textural observations and chemical analyses of crys-tals and glass were done at “Service Microsonde Sud” (Université Montpellier 2) using a five-spectrometer CAMECA SX100 electron microprobe. The analyses were undertaken at 20 kV accelerating voltage, a beam current of 10 nA, and counting times of 20–30 s. Concentrations are obtained from raw intensities using the “X-PHI” quantifi-cation procedure [Merlet, 1994] and standards of natural minerals, synthetic oxides, and pure metals. The spots to be analyzed were selected in the backscattered electron (BSE) mode to ensure that only single phases were analyzed and to facilitate the identification of phases and compositional zoning.
[9] Element detection limits are a function of phase com-position, volatile contents, the surface polish of thin sections, and grain size. Phase identification and characterization of
microstructures were done using an FEI Quanta 200 SEM operating in BSE mode; additional observations were done in a CamScan X500FE CrystalProbe, Electron Back-scattered Diffraction microscope to identify phases, to examine the crystallographic orientation, and to elucidate rock texture. Crystal indexing was performed both manually and automatically. Detection of orientation is possible in grains larger than 0.1 micron, depending on surface polish, thickness of the thin sections, and presence of glass.
3.
Starting Material
3.1. Glassy Basalt
[10] The first suite of glassy basalt (GB) samples came from the caprock of the Deves lava flow, Sénouire valley, France, a microlithic, porphyritic basalt containing about 20 vol % phenocrysts of clinopyroxene and olivine. The remaining groundmass contains phonolitic glass (15–25 vol %) and fine-grained crystalline phases including plagioclase (24–32 vol % of the total rock), clinopyroxene (32–40 vol %), and other oxides (4–8 vol %) (Figure 1 and Table 1). This
modal composition is uniformly distributed at the thin-section scale. The glass component could be identified by the presence of potassium, which is segregated into that phase. By contrast, the crystalline silicate and oxide phases contain less than 0.1 wt % potassium. Thus, the glass quantity was estimated by calculating the mass balance of potassium oxide between bulk rock and glass:
K2O
½ bulk rock= K½ 2Oglass¼ Glass½ bulk rock ð1Þ
Glass abundance was also determined by point counting on optical thin-sections (minimum 300 points per thin section). Both methods suggest that these rocks contain 20 5 vol % glass.
[11] The olivine phenocrysts are subhedral, equant glo-merocrysts of Fo79; these are typically 1–2 mm in diameter, corroded at their peripheries and partially altered to iddeng-site. The clinopyroxene phenocrysts are subhedral laths or prisms of augite that are, on average, 1 mm in length. Com-positional zoning of titanium within the orthopyroxene crystals is very common. In the clinopyroxene phase,
e
Figure 1. Thin-section photographs of (a–c) GB and (d, e) GFB starting sample at different scale. Figures 1a, 1b, 1d, and 1e show thin sections on optical plane-polarized light micrograph. Figure 1c shows Backscattered Scanning Electron microphotograph. Ol: olivine, Cpx: clinopyroxene, Plag: plagioclase, Mag: magnetite, Ap: apatite, Leu: leucite.
VIOLAY ET AL.: BRITTLE-DUCTILE TRANSITION OF BASALT B03213 B03213
groundmass crystals are slightly more titaniferous than phe-nocrysts. The grain size of the clinopyroxene phase present in groundmass is10–100 mm. Plagioclases are subhedral to euhedral labradorite laths up to 100 mm long. Oxides are mainly titanomagnetite, with a few ilmenites. The EPMA analyses indicate that the glass fraction contains about 2–3% of volatiles. Thermo-gravimetric measurements up to 1200C show that the GB samples contain 0.6 wt % volatiles. Thermo-gravimetric measurements did not detect the tem-perature of the glass transition in GB glass. The glass also contains microliths, less than 10mm long, of titanomagnetite, ilmenite and apatite. The starting material does not con-tain hydrous minerals. Porosity was measured by using the classical triple-weighing method. Samples were first weighed after being dried in an oven at50C (>72 h) and re-saturated for“wet” weight measurements in vacuum and immersed in water, flooding the accessible connected porosity. Porosity is 2.4% 0.2%. (Figure 1 and Table 1). 3.2. Glass-Free Basalt
[12] A second set of samples, which are glass-free (GFB), were taken from columnar basalts in the Escandorgue flow, Languedoc-Roussillon, France. These rocks are micro- to crypto-crystalline basalts containing approximately 5 vol. % of phenocrysts (essentially clinopyroxenes and a few oli-vines). Thermo-gravimetric measurements up to 1200C show that the GFB samples do not contain volatiles. The remaining fine-grained groundmass (Figure 1 and Table 1) is a homogeneous mixture of plagioclase (35–45 vol. % of the total rock), clinopyroxene (25–35%) feldspathoids (10%), and titanomagnetite (5–15%). Olivine phenocrysts are sub-hedral, equant glomerocrysts of Fosterite (Fo79), about 300 mm in diameter. Clinopyroxene (Cpx) phenocrysts are subhedral laths or prisms of augite, about 100 mm long; compositional zoning of titanium is very common. Clin-opyroxene crystals in the groundmass (grain size 10– 100 mm) are slightly more titaniferous than clinopyroxene phenocrysts (grain size200–500 mm). In the groundmass, plagioclases are subhedral laths with composition varying from labradorite to oligoclase. The feldspathoids are euhe-dral laths of leucite and nepheline, averaging 50 mm in length. Over scales less than 1 mm, there is local preferred orientation of the feldspathoid and plagioclase crystals, probably due to magmatic flow (Figure 1 and Table 1). Porosity measured by triple weighing is (2.3%).
4.
Mechanical Data
[13] We conducted 34 triaxial deformation experiments under various conditions of T, Pc, Pp, and strain rate
(Table 3). The reproducibility of strength measured in sets of experiments performed at nominally identical conditions indicates sample-to-sample variability (due to porosity, and petrological variability) of about 50 MPa for both GB and GFB sample suites, a value well above the precision of 2 MPa (Figures 2e and 2f). Strength values quoted in the following sections are for constant strain rate of 105 s1, unless stated otherwise.
[14] To simplify the results section we will only present the experiments where Pp= 0 MPa. Others results (Pp≠ 0)
are given Table 3 and Figures 6 and 7. 4.1. Glassy Basalt
[15] In the vitreous samples, elastic behavior at very low strains is followed by one of four deformation modes, depending on temperature, pressure and strain rate (Figures 2a and 2b):
[16] 1. At 400C and confining pressure (Pc) of 100 MPa,
the sample (GB1) yields at about 350 MPa, and then rapidly hardens to peak stress of 900 MPa at strain of 5%, followed by strain weakening (Figure 2a).
[17] 2. Between 500C to 700C (GB2, GB3, GB9), at a confining pressure of 100 MPa, samples yield at stresses that depend on temperature, followed by modest, monotonic hardening up to stresses of 200 20 MPa, at strains of 10%. The strength of the samples at the end of the experiment also depends on temperature, although there is one discrepant result at 700C (Figure 2a).
[18] 3. In one experiment at 800C and Pc = 100 MPa
(GB12), the strength was inversely proportional to strain rate, and this sample exhibited localization and may also have been strain weakening (Figure 3a). Other samples deformed at 800C (GB10, GB11) harden monotonically with strain and exhibited distributed deformation. Strain rate stepping experiments at 800C and Pc= 100 MPa indicate
that strength is directly correlated with strain rate even when a constant hardening coefficient is assumed (Figure 3b).
[19] 4. At 900C, at Pc = 100 MPa (GB14), or between
600–900C at P
c= 300 MPa (GB16, GB17, GB19, GB20),
peak strengths at the end of the experiment are from 30 to 100 MPa. The samples harden monotonically with strain at all temperatures, but the hardening coefficient systematically decreases from 600 to 750C and becomes small at higher temperatures (Figure 2b).
4.2. Glass-Free Basalt
[20] For the glass-free samples, yielding occurs at strains larger than the GB samples, but which are still <2%; yield is followed by one of two deformation modes, depending on temperature and pressure (Figures 2c and 2d):
Table 1. Mineralogical and Petrophysical Characteristics of GB and GFB Samples
Sample Phenocrysts Mineralogy Phenocrysts Grain Size Groundmass Mineralogy Groundmass Grain Size Percentage of Glass Percentage of Alteration Secondary Minerals Porosity (%) Density GB clinopyroxene; olivine 1–3 mm; 1–2 mm plagioclase; clinopyroxene; oxides ≈50–200 mm; ≈10–100 mm; ≈2–10 mm ≈15–25% 1–3% iddingsite 2.4% 3.0 GFB clinopyroxene; olivine 500mm–1,5 mm; 200–500 mm plagioclase; felspathoid; clinopyroxene; oxides ≈20–80 mm;≈30–70 mm; ≈10–100 mm; ≈2–10 mm ≈0% 1–3% iddingsite 2.3% 2.9
[21] 1. Between 600–900C (GFB1, GFB2, GFB3, GFB4, GFB6) at Pc= 100 MPa, or between 600–800C at 300 MPa
(GFB7, GFB8, GFB9), the peak strength depends directly on temperature, but the effect of pressure is not so easily characterized. Peak stress is systematically followed by strain weakening up to strains of about 5–10% (Figures 2c and 2d). Strain rate stepping tests suggest that strength has low strain rate sensitivity, but the strength is also evolving with strain during the experiment, complicating the inter-pretation (Figure 3c).
[22] 2. At the highest temperatures, 800C to 950C (GFB10, GFB11, GFB12 and GFB13), and Pc= 300 MPa, the
peak strength clearly decreases with T (Figure 2d), and hard-ening coefficients are low. Strain rate stepping experiments suggest that strength has low strain rate sensitivity (Figure 3d).
5.
Deformation Textures and Microstructures
[23] After experiments, thin sections were cut so that they contained the shear direction and the sample axis; these were studied using optical, Scanning Electron (SEM) and
Electron backscattered diffraction (EBSD) microscopy (see methods and Figures 1, 4, and 5).
5.1. Glassy Basalt
[24] At lower confining pressures, e.g., 100 MPa and 400 < T < 800C (Figure 4, first column), strain was local-ized, often along a main fault associated with smaller sub-parallel or intersecting cracks and faults. At the lowest pressure and temperature (100 MPa, 400C), glassy basalt samples failed by axial wedge splitting. At 500 < T < 700C, anastomising shear bands about 100 to 500 mm thick developed. Their thickness increased as Pc decreased or T
increased. Most of the shear bands were oriented between 30 and 40 to the compression direction, the angle increasing as temperature increased. Within the shear zone, a cataclastic foliation developed by grain-size reduction, micro-cracking, and rigid-rotation and frictional sliding of fragments (Figure 4, second and third columns). The fault zones contained angular fragments ranging from 0.01 to 10mm; the faults became irregular in shape and orientation when they intersected phenocrysts. Some phenocrysts in or Figure 2. Differential stress versus strain curves for experiments conducted at temperature between
400 and 900C and confining pressure from 100 to 300 MPa. The initial strain rate for all experiments was 105 s1. (a) GB sample at 100 MPa, (b) GB sample at 300 MPa, (c) GFB sample at 100 MPa, (d) GFB sample at 300 MPa (e) GB reproducibility, and (f) GFB reproducibility.
VIOLAY ET AL.: BRITTLE-DUCTILE TRANSITION OF BASALT B03213 B03213
near the shear zone were broken en échelon. Another notable phenomenon was the disappearance of opaque impurities in olivine grains (iddingsite), and the appearance of gray halos on the boundary of some titanomagnetite (Figure 4).
[25] At the highest temperatures and pressures (Pc =
100 MPa and 800 < T < 900C; or Pc= 300 MPa and 600 <
T < 900C), macroscopically distributed deformation was observed. But, even at the highest temperatures, the char-acteristic features of intracrystalline deformation rarely observed. At 600 < T < 800C and Pc= 300 MPa, the glassy
basalt deformed by a combination of diffuse micro-cracking of minerals and the glassy groundmass (at 600C) (image 6 in Figure 4). Cracks were often oriented between 30 and 40to compression direction, and this angle increased as the temperature increased. Accepting the alteration of the iddingsite and titanomagneitite phases mentioned above, metamorphic changes in the other major phases were diffi-cult to recognize because of the wide compositional varia-tions in the starting materials. For example, pyroxene and feldspar crystals are often zoned. However, samples deformed at 100 and 300 MPa and 800 < T < 900C, show evidence that the glass partially recrystallized to biotite and nepheline, a change accompanied by the disappearance of oxides initially contained in the glass and the destabilization of augite. The dark mica now occurs as subhedral laths or spheres ≤ 0.5 mm, and the nepheline crystals are anhedral
and less than 0.3mm in diameter (Figure 4, fourth column). Due to their very small size, the micas and nepheline crystals were difficult to analyze by EPMA. The glass volume frac-tion did not change during deformafrac-tion, but the chemical composition of the residual glass did change as function of temperature (cf. Tables 2–3). At 900C, the Fe2O3and CaO
contents increased by 6.2% and 2.8%, respectively, while NaO and Al2O3 contents decreased by 4.2% and 5.4%,
respectively. These changes are coherent with the mineral-ogical observations: partial dissolution of augite released calcium, aluminum and sodium oxides, which then crystal-lized as nepheline.
[26] Using an SEM at Geosciences Montpellier, we performed Electron Backscattered Diffraction (EBSD) observations to measure the effect of deformation on the crystal-preferred orientations (CPO) of clinopyroxene and plagioclase. Three maps of about 1 mm2were made for each of three thin sections: the starting material and samples deformed at 300 MPa and 600C or 800C. The automatic mapping used a regular grid step of 1 mm, which is about 100 times smaller than the largest observed matrix grains. Map locations were chosen to sample the GB groundmass and to avoid phenocrysts. The automated process success-fully indexed about 35–45% of the pixels. That fraction could be increased to 50–60% by manual indexing, but the CPO patterns obtained automatically and manually were the Figure 3. Differential stress versus strain curves for experiments conducted at different strain rates in
same. Non-indexed pixels were usually located on regions of poor polishing, grain boundaries, glass, or unexpected minor phases like apatite.
[27] The clinopyroxene CPO in the starting material had density maxima for [100], [010] and [001] that were, respectively, 1.8, 1.3, and 1.7 times that of a uniform dis-tribution. Plagioclase CPO maxima in the undeformed samples were 3.2, 4.8, 2.8 times random. Pole densities for both plagioclase and clinopyroxene decreased as the defor-mation temperature increased from 600 to 900C. At 900C, plagioclase maxima decreased to 1.8, 2.3, 1.7, for [100], [010], and [001]. The clinopyroxene maxima decreased more modestly: 1.5, 1.3 and 1.7. The subsequent clinopyr-oxene grains appeared to have rotated, and, indeed, the CPO suggests a rotation of 45 for [100] and [010], but the azimuth of [001] did not change.
5.2. Glass-Free Basalt
[28] The transitions in failure mode in the glass-free basalt were generally similar to those in the glassy basalt, except that localized deformation in GFB was favored to higher
pressure and temperature. When Pc= 100 MPa, deformation
was localized at all temperatures; when Pc = 300 MPa,
localization also occurred at 600 < T < 800C (Figure 5, columns 1–4). Deformation was distributed only when 800 < T < 950C and Pc = 300 MPa.
[29] At 400 to 700C, axial wedge-splitting occurred for all Pc. At 800 to 900C at 100 MPa and 600 to 700C at
300 MPa, GFB samples failed by forming localized, en échelon, shear fractures. These shear zones were oriented between 30 to 45 to the compression direction and contained brittle cataclastic micro-structures (Figure 7c). The angular fragments in the shear zones are now between 0.01mm to 10 mm in diameter, reduced from the initial grain size of 100–500 mm. Shear zones are wider in the center of the sample than near its outer surface. Within the zones, plagioclase and oxide grains are aligned, forming black and white mottling. Oxides are strongly elongated and a series of cracks formed along the edge of the thin section (Figure 5, second column).
[30] At the highest pressure, 300 MPa, and temperatures, 800C to 950C, deformation was distributed. Indications of Figure 4. (a) Photographs of post-run jacketed GB sample (b) thin section photograph of GB samples
deformed under different physical conditions. Images 1 and 5 show optical plane-polarized light micro-graph; images 2–4 and 6–8 show Backscattered Scanning Electron microphotograph.
VIOLAY ET AL.: BRITTLE-DUCTILE TRANSITION OF BASALT B03213 B03213
intracrystalline deformation are rare, and no compositional or mineralogical changes were recognized. Oxides did not show textural or chemical changes (Figure 5, fourth col-umn). Each sample contained a network of interpenetrating micro-faults oriented between 30 and 40. Also, the porosity decreased by about 1–2%.
6.
The Brittle and Ductile Domains
6.1. General Remarks About Mechanism and Mode of Semi-brittle Deformation
[31] To provide generalized formulations of rock strength, researchers often use a few simple constitutive laws meant to describe deformation by a single mechanism [Kohlstedt et al., 1995]. These largely empirical laws are often derived from low-temperature tests of compact rocks, i.e., rocks with low porosity and without partial melts. For example, the shear stress,t, necessary to cause sliding along a pre-existing fault at relatively low temperatures is given by Amonton’s rule:
t ¼ C þ msn ð2Þ
wherem is the coefficient of friction, C is a constant, and snis
the normal stress on the fault [Paterson and Wong, 2005]. Byerlee [1978] discovered that m is relatively insensitive to rock type, at least at low temperatures without added fluids. Thus, he proposed that a simple combination of two linear equations of the form (1) could be used to constrain frictional sliding in natural situations.
[32] Brittle failure by localized rupture in compact rocks at low temperatures can be described using the Coulomb fail-ure criterion [Lockner, 1995]. Thus, under conventional tri-axial loading, the peak differential stress,s1–s3, is related to
confining pressure, Pc, by
s1 s3
ð Þ ¼ soþ m′Pc ð3Þ
wheres2=s3= Pc. The constants,m′ and so, can be
trans-formed to relate shear stress and normal stress on the rupture plane, yielding an equation of the form equation (3). The transformed constants are the internal coefficient of friction, mc, and the cohesive strength, Ccoh, and are related tom′ and
so[Paterson and Wong, 2005]:
mc¼ m′= 2√ 1 þ m′ð Þ ð4Þ Ccoh¼ s0= 2√ 1 þ m′ð Þ ð5Þ
Table 3. Summary of Experimental Conditions and Resultsa
Run T (C) Peff (MPa) Strain Rate (x 105s1) Peak Strength ors at 2% (MPa) s at 5% (MPa) Stress Evolution GB 1 400 100 1 915 910 S GB 2 500 100 1 230 276 H GB 3 600 100 1 150 200 – GB 4 600 70 1 290 235 H GB 5* 600 50 1 225 – S GB 5* 600 70 1 – 225 – GB 6* 600 100 1 226 H GB 6* 600 100 0.1 220 – GB 7* 600 50 1 140 – H GB 7* 600 50 0.33 – 150 H GB 8* 650 200 1 112 – H GB 8* 650 250 1 – 130 H GB 9 700 100 1 169 265 H GB 10 800 100 1 50 54 H GB11* 800 100 1 70 90 H GB 12* 800 100 1 40 – S GB 12* 800 100 5 – 45 – GB13 900 100 0.1 35 50 H GB14 900 100 1 55 50 H GB 15* 900 100 1 20 – H GB 15* 900 100 5 – 25 – GB 16 600 300 1 101 160 H GB 17 700 300 1 67 110 H GB 18 750 300 1 46 70 H GB 19 800 300 1 48 60 H GB 20 900 300 1 40 45 H GB 21* 900 300 1 35 – H GB 21* 900 300 5 – 35 – GFB 1 400 100 1 1026 – S GFB 2 600 100 1 872 – S GFB 3 700 100 1 550 – S GFB 4 800 100 1 473 – S GFB 5* 800 100 1 450 S GFB 5* 800 100 0.5 – 248 – GFB 6 900 100 1 414 215 S GFB 7 600 300 1 704 – S GFB 8 700 300 1 646 692 – GFB 9 800 300 1 506 485 S GFB 10 800 300 1 520 590 H GFB 11 850 300 1 386 450 – GFB 12* 900 300 1 274 288 – GFB 13* 950 300 1 123 – – GFB 13* 950 300 0.5 – 80 –
aColumn 1: Experiment run. Runs with an asterisk: strain rate stepping
tests. Column 3: Effective confining pressure. Peff= PcPp, Peffis the
effective pressure. Pc is the confining pressure. Pp is the pore fluid
pressure. Column 5: For stress–strain curves showing weakening, this corresponds to the peak stress. For strain hardening curves, we report s1s3 at 2%. Column 6: we report s1s3 at 5% of effective strain.
Column 7: Mode. W: Strain weakening aftersmax and localization; H:
Strain hardening.
Table 2. Chemical Composition of the Glass of GB Starting Material and GB Deformed Samples
Sample
Total SiO2 Al2O3 TiO2 Na2O MgO MnO FeO K2O CaO
Starting material 51.28 23.69 1.31 9.47 0.80 0.10 4.82 5.57 1.07 98.30 Deformed sample at 600C 50.06 23.07 1.62 8.74 1.22 0.13 6.61 4.95 1.55 98.20 Deformed sample at 700C 49.75 20.43 2.23 5.84 2.34 0.14 6.46 4.30 6.26 98.25 Deformed sample at 800C 50.32 18.86 1.38 2.38 2.12 0.10 9.72 8.02 2.68 97.20 Deformed sample at 900C 52.48 18.23 2.66 5.26 1.73 0.15 11.21 4.99 3.85 100.67
At high T and Pc, when cataclasis can be neglected,
dislo-cation creep may be important and is often represented by a steady state power law:
_ɛ ¼ A:sn:exp Q=RTð Þ ð6Þ
where A is a material constant, n, the stress exponent, Q, the activation energy, R, the gas constant. All of these consti-tutive laws are rough generalizations that neglect many possibly important state variables, including fluid chemistry, pore geometry, and evolution of the structure of the solid [Evans, 2005].
[33] The transition from one mechanism to another may be gradual. As Pcand T increase, cataclasis is suppressed, and
intracrystalline defect migration is enabled. Thus, the aggregate rock strength becomes less sensitive to confining pressure and more sensitive to temperature and strain rate. Pressure sensitivity is usually very low when rock strength is less than the confining pressure, an empirical observation called the Goetze criterion [Kohlstedt et al., 1995]. In the region ins, Pcspace between Byerlee’s rule and the Goetze
criterion, deformation in dry compact rocks is often distrib-uted, and strain accommodated by a combination of cata-clasis and intracrystalline mechanisms.
[34] A similar framework for the change in failure mode from macroscopically localized, brittle fracture to ductile, non-localized flow can be formulated [Heard, 1960; Evans et al., 1990; Paterson and Wong, 2005]. Here, we use the term“ductile” simply to denote the capacity of a sample to deform without localized faulting [cf. Paterson and Wong, 2005; Rutter and Neumann, 1995], not to imply isochoric strain, or that any particular deformation mechanism oper-ates. Notice that this definition is a macroscopic character-ization of the aggregate deformation, as are stress-strain measurements.
[35] Localized brittle failure in compact rocks without melt typically occurs under conditions of T and Pc, where
the peak strength, given by the Coulomb failure criterion, is greater than that required to cause slip on an optimally ori-ented fracture, as given by Byerlee’s rule (see equation (2) and Figure 6). The distinction between brittle and ductile deformation modes may be quite complicated, particularly Figure 5. (a) Photographs post-run jacketed GFB sample. (b) Microstructures of several deformed GFB
samples of basalt on thin sections. Image 5 shows optical plane-polarized light micrograph; images 1–4 and 6–8 show Backscattered Scanning Electron microphotograph.
VIOLAY ET AL.: BRITTLE-DUCTILE TRANSITION OF BASALT B03213 B03213
for multiphase materials, because the transition from one mode to another may be gradual, and because different phases might exhibit different failure modes at the same time. All of the remarks above, regarding both mechanism and mode, are great simplifications and rough general-izations. But, they may be used as a framework to analyze more complex mechanical behavior, like the semi-brittle deformation observed in these basalt samples.
6.2. Deformation Mode and Mechanisms in Basalt at High T and P
[36] Changes in the deformation mode roughly correlate with the stress-strain behavior in both suites of samples, as predicted by the generalized framework. In glassy samples, localization was accompanied either by strain weakening or by deformation at nominally constant stress (500–800C, 100 MPa); while distributed deformation was always accompanied by strain-hardening. In the glass-free basalt, localization always corresponded to strain weakening, whereas distributed deformation occurred at constant stress. As expected, the degree of localization and grain commi-nution in both basalts decreased with increasing pressure and temperature. For GB, at 400C, 100 MPa, localization was intense, whereas at 500C < T < 800C and 100 MPa, rup-ture occurred along broader zones of crushed grains. In the GFB, as P and T increased, the failure mode changed from wedge splitting (400–600C, 100 MPa), to shear rupture (700–900C, 100 MPa, or 600–800C, 300 MPa), finally to homogeneous flow (800C, 300 MPa). It is sometimes dif-ficult to identify the relative activity of various deformation mechanisms. Characteristic microstructural fingerprints of intracrystalline mechanisms are not evident from the optical and SEM observations used here. Brittle mechanisms are less circumspect. For example, cataclasis was certainly involved in the deformation of the GB sample at 600C 300 MPa. In those samples that contain a glass phase, it is possible, if not likely, that the glass might be mobile at the higher temperatures, but not leave microstructural evidence. [37] There were, however, significant differences from the generalized framework shown by the mechanical behavior of both sets of samples. For these experimental conditions, the strength of basalt was affected by strain rate, _ɛ, finite strain,ɛ, absolute temperature, T, and confining pressure, Pc,
and none of the end-member constitutive laws accurately describes all of the data for either the GB or GFB samples, which deformed by mixed mechanisms in a semi-brittle regime [Paterson and Wong, 2005]. Also, notice that our axial compression tests were limited to strains <15%. Thus, one does not know if weakening, hardening, or a steady state would occur at higher strains. Moreover, precise yield points marking the departure from linear behavior were not always obvious. Finally, the initial, presumably elastic domain of the stress-strain curves varied from one experiment to another. Given these complexities, we explicitly describe the effect of each physical parameter on strength.
6.3. Effect of Confining Pressure
[38] The brittle-ductile transition in basalt is favored by increases in Pc and T. For the GB samples at 100 MPa,
brittle failure occurs at 400 to 700C, while ductile behavior only occurs at 800–900C. At 300 MPa, ductile behavior begins at 600C. GFB samples are brittle at 400–900C and
100 MPa, and at 600–700C and 300 MPa; ductile behavior occurred between 800 and 950C at 300 MPa. For the GFB, at 100 MPa, deformation localized at all temperatures, also at the highest temperature (900C), i.e., localized failure persisted to higher temperatures than predicted by Byerlee’s rule (Figure 6). At PC= 300 MPa, the transition to ductility
occurs within the semi-brittle field, but still at higher tem-peratures than expected (800C to 850C). It is important to mention that the transition in mode will probably depend on strain rate, which in our experiments was limited to the range 104 106 s1. For GB samples, the change of strength with increased Pcwas small or even negative. Strengths at a
strain rate of 105s1, 400 < T < 600C, and Pc= 100 MPa
were large: from 900 to 250 MPa. When Pc = 300 MPa,
strengths never exceeded 100 MPa. At these conditions, all strengths were well below the confining pressure and defor-mation was distributed, consistent with the Goetze criterion. [39] In Figure 7 we plot the sliding stress, at 5% perma-nent strain, after stress drops had occurred, and, presumably, when strain had localized along a rupture plane (Table 3). Notice that the sliding stress for both GB and GFB samples depends strongly on effective pressure at all temperatures. The friction (sliding) coefficient was determined from pres-sure dependence of steady state sliding strength (character-ized by a constant value of differential stress) (Figure 7a). The coefficient of friction at a strain of 5% is similar for GB and GBF samples.
6.4. Temperature Dependence
[40] In the brittle (localized) domain, the peak fracture strength of the glassy basalts depends only sensitively on T, except at the lowest temperatures (400C) where samples were very strong. At 100 MPa and 600C, the peak strength is scattered, apparently owing to sample-to-sample variabil-ity (Figure 6). Sliding stress values also show scatter of order 50% (Figure 7). For the glass-free samples, both peak strength (Figure 6) and the sliding stress at 5% (Figure 7) showed systematic, but modest, decreases with temperature in the intervals 700–900C at 100 MPa and 600–800C at 300 MPa (0.5 MPa/C). GFB samples at 400C and 600C and 100 MPa were quite strong (Figure 6). In the ductile (distributed) domain at strain up to 8%, the strength of both GB and GFB samples decreased systematically with the temperature (>20 MPa) (Figures 2 and 6). The tempera-ture dependence of the GFB samples was greater than the GB series (cf. Figure 8), where we plotted the logarithm of strain rate versus the inverse of temperature for Pc= 100 MPa). Q,
the activation energies of the GB and GFB are 59 kJ.mol1 15 and 456 4 kJ.mol1respectively (see section 7.2). 6.5. Strain Rate Dependence
[41] In the brittle domain, the peak strength of both GB and GFB samples depended weakly on strain rate (Figures 3 and 9). Notice the marked difference in strain rate sensitivity between samples with localized and distributed deformation, particularly for the glassy samples. GB samples with local-ized deformation had small or even slightly negative strain rate sensitivity (Figure 9), but their peak strength still decreased with T over the range 600 to 800C. When strain was distributed, the strain rate sensitivity of strength was much more pronounced, increasing with temperature. The temperature effect was larger for the GFB. Stress-relaxation
Figure 6. Strength versus pressure for 400C < T < 950C. Peak stresses are reported for samples that localized, and the differential stress at 2% strain for samples that showed distributed deformation. Open symbols indicate localized deformation; full symbols had distributed deformation. Byerlee’s rule and the Goetze criterion are given as references.
Figure 7. Maximum differential stress increases with effective confining pressure for brittle deformed samples. On the strain-stress curves, the stress value is picked at 2% after stress drop. (a) Linear trend of effective confining pressure versus friction stress at strain rate of 105 s1. (b) Mohr circle con-structed with the data presented on Figure 3a. The line approximately tangent to the Mohr circles indi-cates a coefficient of frictionm = 0.42 and C = 34 MPa. (c) Cracks orientations versus pressures for GFB sample.
VIOLAY ET AL.: BRITTLE-DUCTILE TRANSITION OF BASALT B03213 B03213
tests generally agree with constant strain rate tests, but both types show scatter, probably reflecting sample hetero-geneities and sample-to-sample variability.
6.6. Finite Strain Dependence
[42] The peak strength of the GB sample at 400C and Pc= 100 MPa and GFB sample at 400C and 600C is
fol-lowed by a load drop and then strain weakening (Figure 2). At 300 MPa, GB samples hardened at all strains and tem-perature, but the hardening rate systematically decreased from 600 to 750C, becoming very small at higher T (Figure 2b).
6.7. Tentative Constitutive Laws 6.7.1. Brittle (Localized) Behavior
[43] The peak strength in the localized regime for both GB and GFB samples is only weakly sensitive to strain rate.
Similarly, the sliding strength, after the load drop, is insen-sitive both to strain or strain rate, roughly consistent with the generalized view presented in section 6.1. But, the pressure sensitivity of peak strength, especially of the GB samples is inconsistent with that view. In addition, the glassy basalt strength is temperature sensitive (Figure 9). The friction coefficient was determined from Mohr circles plots mea-sured at _ɛ = 105 s1 (Figure 7b). A linear fit between s1–s3and Peff gives a slope m′ = 1.3 and so = 106 MPa.
From equation (4), the coefficient of friction,m = 0.42 and cohesive strength Coh = 34 MPa. The fracture angle
char-acteristic of these parameters is of 33 to the compression direction, which corresponds to our observations on GFB at 100 MPa (600C–900C) and 300 MPa (600 and 700C) (Figure 7c). These values are lower than those suggested by Byerlee [1978] (t = 50 + 0.6.sn), but agree with previous Figure 8. Plots of stress versus the reciprocal temperature at different finite strain. (a) GB sample.
studies on various volcanic rocks at low temperature (0.43 < m < 0.6) [Rocchi et al., 2003].
6.7.2. Ductile (Distributed) Behavior
[44] The behavior in the ductile field is more difficult to describe, probably owing to the operation of both cataclastic and intracrystalline deformation mechanisms or to redistri-bution of melt. Failing a detailed mechanical description of semi-brittle flow, we analyze strength in the ductile regime by computing effective parameters using the power law (equation (6)). Using this constitutive law will be an approximate lower bound of the actual rock strength, in the
case of work hardening, or an upper bound in the case of strain softening, even without extrapolation. It is clear that a more accurate constitutive law is necessary to describe the basalt behavior at conditions different than those tested here. [45] To determine the apparent n, Q, and A for equation (6), we used only results between 700C and 900C and at confining pressure of 300 MPa for glassy samples. For GFB, we used data only between 850C and 950C at a confining pressure of 300 MPa. The strain rate dependence was determined from strain rate-steps and stress relaxations that were applied in most runs (Figures 3 and 9; Table 3). Figure 9. Plots of log strain rate versus log stress. (top) GB sample, (bottom) GFB sample. Open
sym-bols correspond to localized deformation. Full symsym-bols correspond to distributed deformation. Symsym-bols are strain rate stepping tests. Solid lines are stress relaxation tests.
VIOLAY ET AL.: BRITTLE-DUCTILE TRANSITION OF BASALT B03213 B03213
Additional creep tests were performed at constant stresses of 70 MPa and 100 MPa and confining pressures of 300 MPa. Stress exponent n was determined from linear regression of log (stress) versus log (strain rate) at each temperature (Figure 9).
[46] For GB, the stress exponent (n) ranges from 3.1 to 4.3. For the GFB, n ranges from 3.0 to 4.2. The activation energy was determined from a least squares fit of log (stress) versus 1/T at a given strain rate, or by correcting the strain rates to a given constant stress of 100 MPa at each temper-ature and fitting the logarithm strain rate versus inverse temperature (Figure 8). The strength at 5% was used unless strength continued to evolve. Then, the activation energy was also calculated at different strains.
[47] For glassy samples, the activation energy is weakly dependent on finite strain and was 59 15 kJ/mol, a rela-tively low value when compared to diabase or feldspar rocks without melt. For glass-free basalt, the activation energy is independent of the finite strain. The fact that activation energy and stress exponents do not evolve during experi-ments for GFB and only slightly for GB samples suggests that the relative activities of the various deformation pro-cesses evolve slowly over this strain interval. However, there is a considerable difference in the apparent activation energies of the GB and GFB: 59 kJ.mol1 15 and 456 4 kJ.mol1respectively.
[48] Combining average values for apparent n and Q, the following strain rate laws are calculated (cf Table 4):
GB: _ɛ ¼ 1:3 0:8 * 109sð3:70:6Þ expðð59;015Þ=RTÞ GFB: _ɛ ¼ 6:1 2:2 * 108sð3:60:6Þ expðð456;04Þ=RTÞ
where the stress is in MPa, the activation energy in kJ/mol and the pre-exponential term in MPans1. The large uncer-tainty of the pre-exponential term reflects sample-to-sample variability and heterogeneity, but also owes to the explicit complexity of the actual mechanisms.
7.
Discussion: Strengths of Glassy and Glass-Free
Basalts
[49] In the brittle field, the kinematics of the deformation modes of the glassy and non-glassy basalts are quite similar: In the localized regime, cataclastic rupture planes developed with clear evidence of grain comminution. Peak strengths were reached within a few per cent strain, followed by rapid
weakening. Thereafter, sliding occurred along the rupture planes; during this phase, both glassy and glass-free rocks had roughly the same friction coefficient, 0.4. However, the peak fracture strength and the sliding strength of the glassy basalts were always lower than those of that were glass free. When glass was present, the transition from brittle to ductile modes occurred at a lower pressure. In the ductile domain, the presence of glass was associated with reduced strength, and there was also a large reduction in the apparent activa-tion energy. In contrast, the stress-sensitivity of strain rate, n, was the same for both rocks. Notice that the two sample suites differed in composition only by the amount of glass. Below, we compare the current results to previously pub-lished studies of basalt and diabase, assess the impact of the presence of glass on ductile deformation, and discuss the effect of petrology on strength.
7.1. Mechanical Tests on Glass-Free Basalts
[50] Early mechanical tests were conducted on non-glassy diabases in a solid-medium apparatus by Shelton and Tullis [1981], in a gas apparatus by Caristan [1982], and on syn-thetic gabbros in a gas apparatus by Dimanov and Dresen [2005] and Dimanov et al. [2007]. The Caristan [1982] tests were constant strain rate experiments on Maryland diabase at Pc = 450 MPa, T = 1000C and 2.103 < _ɛ <
4.106. Deformed samples had a combination of brittle and plastic microstructures. It was later discovered that these rocks initially contained a small concentration of alteration minerals, which dehydrated at high temperature, liberated water, formed a small amount of melt, weakened the sam-ples, and promoted stress drops [Evans et al., 1990; Mackwell et al., 1998]. When the diabases were dried at high temperatures, no melt formed during the deformation tests, and they were strengthened [Mackwell et al., 1998]. Creep tests on dried Maryland and Columbia diabases at 900C < T < 1050C, Pc= 500 MPa, and strain rate from 107< _ɛ <
105 s1 indicate the operation of dislocation creep. Strength from the flow laws for diabase at _ɛ = 105s1are plotted versus temperature [Caristan, 1982; Kirby and Kronenberg, 1984; Mackwell et al., 1998] in Figure 11. For comparison, data for GB and GFB are also given.
[51] The diabase strength measured by Caristan [1982] and Mackwell et al. [1998] are higher than that of GFB by a factor of three at 800C, and six at 1100C. The stress exponent in all three studies are similar, but our activation energy is slightly lower than those found earlier (Table 4). Small strength variations might be explained by differences Table 4. Creep Data From Previous Studies on Diabases and Present Study
A (MPa-ns1) n Q (kJ mole1)
Shelton and Tullis [1981] ? 3.4 250
Caristan [1982] (Maryland diabase) 6.1E-2 3.1 270 Kirby and Kronenberg [1984] 1.6E-05 6.4 444 Mackwell et al. [1998] (Columbia diabase) 1.9 1.1E02 4.7 0.6 488 35 Mackwell et al. [1998] (Maryland diabase) 8.0 4.0 4.7 0.8 482 25 Hacker and Christie [1992] (675C–775C) 5.3 1.0E-09 5.4 0.2 263 20 Hacker and Christie [1992] (825C–875C) 1.1 0.1E-05 3.3 0.1 175 30 Dimanov and Dresen [2005] (dislocation creep - dry conditions) 2.7E-12 (+2.6E-10/2.6E-12) 4.1 0.2 723 52 Dimanov and Dresen [2005] (diffusion creep - dry conditions) 6.7E04 (+1.1E06/6.4E04) 1.0 496 34 GB (present study) 1.3 0.8E-09 3.7 0.6 59 15 GFB (present study) 6.1 2.2E08 3.6 0.6 456 4
in the petrology, but the modal and chemical composition of Maryland diabase and the GFB are quite similar. The grain size and crystal shapes of clinopyroxene and plagioclase in the GFB groundmass are also different: groundmass pla-gioclase sizes are heterogeneous and average of 50 mm in length. Augite and plagioclase are frequently xenomorphic. In Maryland diabase, plagioclase size is homogeneous and ≈200 mm. Augite and plagioclase appear pseudo-automorphic [Caristan, 1982]. However, high-temperature dislocation creep in feldspar and pyroxene is usually affected only weakly by grain size [Rybacki and Dresen, 2004; Dimanov and Dresen, 2005; Dimanov et al., 2011]. Chemi-cal effects, including changes in water or oxygen fugacity, can influence both the strength of the crystalline phases, especially pyroxene, and the viscosity of the melt [Giordano et al., 2008]. Accessory phases are one way that volatile fugacities can be buffered, and we note that the oxide content of Maryland diabase is1%, but is 10% in GFB.
7.2. Mechanical Tests on Glassy Basalts
[52] Hacker and Christie [1992] (HC) deformed a glassy plagioclase-rich basalt at T between 675 and 875C, Pc =
1 GPa, and strain rates of 104–107s1in a solid-medium apparatus; those workers cast their results in terms of a power law creep equation with no explicit dependence on melt content (equation (4)). Our apparent stress exponents at 800 < T < 900C are similar to theirs, but our apparent activation energy (59 15 KJ/mol1) is about 3 times smaller (175 30 KJ/mol1) (Table 4). There are several other differences between their samples and ours. The glass content was 10–15% in HC; and 15–25% in GB. The glass composition was rhyolitic for HC; and phonolitic for GB. The plagioclase HC basalt was ductile at all conditions, whereas our samples deformed in both localized and ductile modes. Deformation in HC occurred by a combination of cracking, dislocation glide, and glass flow. Cracks formed Figure 10. Two components models (glass and basalt) calculated in series and parallel at temperature of
700C and 800C for 10%, 20%, 100% of dry melt, 20% of hydrated (1% of water) melt. Glass rheology is derived from Whittington et al. [2001]. Basalt rheology is derived from GFB power flow law. GB rheol-ogy is given as reference (shaded area).
VIOLAY ET AL.: BRITTLE-DUCTILE TRANSITION OF BASALT B03213 B03213
into a network of micro-faults inclined at 40–50 to the compression axis, a similar geometry to that observed in our samples.
[53] Many previous studies in a variety of partially molten rocks, indicate that aggregate strength depends on the melt fraction, fm, the distribution of the melt [Arzi, 1978; Hirth
and Kohlstedt, 1995; Scott and Kohlstedt, 2006; Van der Molen and Paterson, 1979; Dimanov et al., 1998, 2000], and the capacity of the melt to migrate [Dell’Angelo and Tullis, 1988; Holtzman et al., 2003; Renner et al., 2000]. For example, in partially molten peridotite at T > 1200C, where melt is well-connected at almost all degrees of partial melting, strength decreases by 2.5 orders of magnitude over the interval, 0 <fm< 0.20 [Scott and Kohlstedt, 2006]. The
apparent stress sensitivity, n, and activation energy, Q, in the dislocation creep regime do not depend on melt content, suggesting that the effect offmcan be incorporated into the
flow low as a separable function: _ɛ ¼ A′snexpaf
m
ð Þ exp QRT
ð7Þ
where A′ and a are empirical material constants, and n and Q are the same as for peridotite without melt. For the basalts, under the conditions of our experiments, apparent n values for GB and GFB samples are similar, but the apparent acti-vation energies are quite different, a complication not admitted by equation (7).
[54] Melt migration is also an important aspect for the mechanical behavior. At low strain rates or if melt is well connected, migration will promote ductile deformation and may favor inter-granular flow or diffusion creep. At high strain rates, or when poorly connected, the melt may be effectively undrained, thus, promoting brittle deformation [Ko et al., 1997; Renner et al., 2000]. We did not directly observe deformation or migration of the glassy phase. However, EBSD results in the GB sample deformed at 900C suggest that deformation was associated with a weak disorganization of the initial crystalline fabric, and that clinopyroxene crystals throughout the sample rotated with respect to the compression axis. The lack of evidence of dislocation creep is also consistent with rigid rotation. Thus, the deformation kinematics might be described, at least tentatively, as relatively large rigid crystals rotating in soft matrix of micro- to nano-sized crystals and glass, a description corresponding to SEM images.
[55] In the interval,fm≈ 0.20–0.40, the strength of
par-tially molten rock evolves from that characteristic of a solid with liquid inclusions, to that of a liquid with solid inclu-sions [Arzi, 1978; Van der Molen and Paterson, 1979; Riley and Kohlstedt, 1991; Rutter and Neumann, 1995; Barboza and Bergantz, 1998; Renner et al., 2000; Rosenberg and Handy, 2005]. The glass content of the glassy samples, between 15 and 25%, is near the lower bound of this rheological transition, suggesting that a simple flow law Figure 11. Plot of differential stress versus temperature. Stresses are calculated for strain rate of 105s1
using a flow law for diabases (black curves) [Mackwell et al., 1998; Caristan, 1982; Shelton and Tullis, 1981] and flow law of GB and GFB (red curves). Experimental points are also given (red points). Flow laws for dislocation creep (green curves) and flow law for diffusion creep (blue curves) of 50%plagio-clase-50%clinopyroxene aggregates with 0.005%Wt water (solid line) and 0.0075%Wt water (dashed line) [Dimanov and Dresen, 2005] are given as references. Flow law for diffusion creep of plagioclase-clinopyroxene aggregates [Dimanov and Dresen, 2005] is given for3 mm grain size with a grain size exponent m = 3.
considering a single mechanism may not be adequate to describe the mechanical behavior of basalt.
[56] As a first small step to include a second mechanism, we treat the rock as an aggregate composed of two separate crystalline and glass phases, using the well-known mixing laws [Clyne and Withers, 1993]:
1 _ɛGB¼ v _ɛGlass þ 1_ɛ v GFB ð8Þ _ɛGB¼ v _ɛGlassþ 1 vð Þ _ɛGFB ð9Þ
where v is the volume fraction of glass in the mixture, and _ɛGB, _ɛGlass, and _ɛGFB are the average strain rates for the
glassy aggregate, the glass phase, and crystalline compo-nent, respectively.
[57] When the creep process in one phase is dependent on each other the processes of other phase they are said to be sequential, in such a case each mechanism participates for a different increment of time. Since the strain contribution of each phase must be identical to maintain aggregate integrity the respective contributions are weighted by their volume fractions as given in equation (8). The physical configuration of such a two-phase system is often idealized as a slab model with parallel layers of the two phases with a homogeneous stress field, sometimes referred to as the Reuss (elastic) or Sachs (plastic) model. The slower process dominates the strain rate, but not the necessarily the strain (and micro-structure), as the slower process must operate and produce strain, so that the faster one can operate in a sequential manner. In contrast, when the creep processes in each phase operate independently each of them contributes to the strain over the entire time increment considered, so that the volume fraction weighted strain rates are additive as shown in equation (9). In this case the strain field in the idealized two-slab is homogeneous and fastest mechanism dominates the strain rate, this type of behavior is called the Voigt (elastic) or Taylor (plastic) model. The Voigt/Taylor behavior should have significant impact on the microstructure.
[58] For strength in crystalline phase we use mechanical results for glass-free basalt (GFB). The EPMA analyses of the glass in the GB samples show that its composition is close to a hydrated phonolitic melt with 1–2% of water. Thus, the viscosity of phonolitic melt have been used [Whittington et al., 2001]. At our experimental temperatures, the viscosity for a dry phonolitic melt varies between 107 and 1021Pa.s, and between 105and 1013Pa.s for a hydrated phonolitic melt [Whittington et al., 2001]. Strengths for the two mixing models were calculated at 700C and 800C, for basalt with dry melt fraction (fm) of 10%, 20%, and for
basalt with melt hydrated with 1% of water of fm= 20%.
The results are plotted in Figure 10 along with data for the GB tests and for phonolitic melts. None of the models mat-ches the GB data completely, but at 700C, the GB strengths are intermediate between the Voigt/Taylor and Reuss/Sachs models for samples withfm= 20%, hydrated with 1% water.
At 800C, the GB rheology is closer to the Voigt/Taylor withfm= 20%, dry or wet. These comparisons suggest that
the water content of melt might be an important aspect of the rheology of the glassy samples. Second, the differences in activation energy between GB and GFB samples suggest
that a process other than dislocation creep, probably having to do with melt migration or deformation, accommodates part of the deformation. In addition to changes in melt viscosity, the strength may be affected by other factors, including changing melt connectivity, local elevations or depression of melt pressure, changes in the proportion or size of crystalline phases within the melt, or fugacity of water. Clearly, a more sophisticated model involving more information on the microstructure would provide better physical constraints on the mechanics of the deformation.
7.3. The Impact of Microstructure and Petrology on Mechanical Behavior
[59] During the tests, biotite and nepheline grew, replacing glass and magnetite in all GB samples deformed at high pressure (300 MPa). Neo-mineralization affected only about 10% of the glass fraction of each sample, and neo-crystals were less than 10mm in length. In parallel, glass chemistry evolves during experiments; in particularly the glass dehy-drates, which implies changes of its viscosity, and hence potential effects on the mechanical response of the glassy basalt itself. Experiments of longer duration are needed to study the influence of metamorphism on the deformation process. However, the crystallization of quartz and mica during Hacker and Christie’s experiments did not seem to affect the mechanical behavior of that glassy basalt. Although we also have no direct evidence that metamor-phism affects deformation mechanisms in our samples, it seems possible that hardening might result from changing melt chemistry or reduction in permeability caused by changes in the crystal fraction of the amorphous phase.
[60] Grain size difference between GB and GFB has a potential impact on deformation at high temperature. Both samples have approximately the same clinopyroxene grain size, but GB plagioclase grain size (50–200 mm), is twice as large as GFB plagioclase grain size (20–80 mm). At high-temperature, dislocation creep in feldspar is usually affected only weakly by grain size, however grain boundary diffu-sion-creep is significantly affected by grain size distribution [cf. Dimanov et al., 1999, 2003, 2007, 2011; Dimanov and Dresen, 2005].
[61] On the Figure 11, the differential stress versus tem-perature is plotted for strain rate of 105s1using the flow laws of GB and GFB, and flow laws for diabases [Mackwell et al., 1998; Caristan, 1982; Shelton and Tullis, 1981]. Flow laws for dislocation creep and flow law for diffusion creep of 50% plagioclase 50% clinopyroxene aggregates [Dimanov and Dresen, 2005] are given as a reference. Flow law for diffusion creep of plagioclase-clinopyroxene aggregates [Dimanov and Dresen, 2005] is given for 3mm grain size with a grain size exponent m = 3, [see Dimanov and Dresen, 2005, equation 1].
[62] The mechanical behavior of GB and GFB at our experimental temperature and strain rate are not compatible with the diffusion creep regime (even for very small grain size), as shown in Figure 11. GFB mechanical behavior is compatible with the dislocation creep regime. Small dif-ferential stress difference between GFB and plagioclase-clinopyroxene aggregates of Dimanov and Dresen [2005], might be explain by difference in petrology (aggregates do not contain oxide, plagioclase is anorthite and not labrador-ite…), and in porosity (aggregates porosity is <1%). GB VIOLAY ET AL.: BRITTLE-DUCTILE TRANSITION OF BASALT B03213 B03213
sample present an additional complexity due the presence of glass. Stress exponents (3 < n < 4.2), for both GB, and GFB samples, could be indicative of deformation dominated by dislocation creep processes. We therefore postulate that plagioclase grain size difference between GB and GFB samples cannot explain their difference in mechanical behavior. However, grain boundary diffusion-controlled process can be a concomitant or co-operational mechanism for grains of very small size and may contribute to defor-mation, in particular in presence of a liquid phase, as sug-gested Dimanov and Dresen [2005]. Further microstructural observations must be done to quantify the importance of the grain boundary diffusion-controlled process on the defor-mation of GB and GFB.
[63] Oxide accessory phases might also be important. The first sign of plastic deformation in GBF sample was the elongation of oxides, parallel to the shear zone boundaries, which occurred at about 700C. At this temperature, plagi-oclases and clinopyroxene deform by combination of micro-cracking and heterogeneous micro-cracking [Kronenberg and Shelton, 1980]. Yet, little is known about the role of Fe-Ti-oxides during shear zone deformation. Agar and Lloyd [1997] have suggested that in nature, magnetite deforms by diffusion creep at T up to 550 to 650C. So, Fe-Ti-oxides behave as highly ductile phases at low temperature [Muller and Siemes, 1972]. Thus, high concentrations of Fe-Ti-oxide in shear zones might significantly reduce basalt strength.
8.
Implication for Oceanic Crust
[64] The strength of oceanic crust, largely composed of basaltic rocks, is a function of temperature, pressure, fluid chemistry, lithology, melt and glass chemistry, and melt volume fraction. Glass is unlikely to persist for long times at depth [Staudigel and Hart, 1983], but is sometimes found at dykes or the margins of magma flows [Ross, 1983; Thy et al., 1985; Fisk et al., 1996].
[65] The brittle to ductile transition in rocks has often been described as a parameter that can influence the absolute permeability value and the porosity topology. The BDT may be an indicator of the maximum depth and temperature at which hydrothermal fluids may circulate.
[66] Indeed, in low porosity rocks, laboratory measure-ments indicate that, for both brittle failure and cataclastic flow, dilatancy (porosity increasing with strain) and perme-ability increase. Permeperme-ability increases monotonically till localized brittle failure occurs [Zoback and Byerlee, 1975; Peach and Spiers, 1996; Zhu and Wong, 1997; Mitchell and Faulkner, 2008; De Paola et al., 2009]. For example, the permeability of Westerly granite increased by a factor of 3 when the sample was stressed to 80% of the peak fracture strength [Zoback and Byerlee, 1975]. In the cataclastic regime, measurements on halite [Peach and Spiers, 1996; Stormont and Daemen, 1992], on Carrara marble, and hot pressed calcite [Zhang et al., 1994] all indicate rapid increases of permeability with the accumulation of several percent strain. Microstructural analyses led to the interpre-tation that the large increase in permeability in the brittle domain is due to a large connected network of intragranular and intergranular microfractures [Brace and Byerlee, 1967; Zoback and Byerlee, 1975; Zhang et al., 1994; Moore and
Lockner, 1995; Peach and Spiers, 1996; Siddiqi et al., 1997; De Paola et al., 2009].
[67] In the ductile domain (distributed deformation), low porosity rocks, can be associated with minor dilatancy or compaction depending of the deformation mechanism. For the cataclastic creep mechanism, in calcite [Zhang et al., 1994]; in quartz-calcite aggregate [Siddiqi et al., 1997]; in anhydrite [De Paola et al., 2009], the ductile deformation is associated with minor dilatancy that leads to a small increase in permeability with increasing finite strain, until it is stabi-lized to a fixed value when a percolation threshold is reached. De Paola et al. [2009] state that the permeability value is lower than the permeability attained immediately prior to failure in the brittle mode.
[68] For others deformation mechanisms such as hydro-static compaction [Bernabé et al., 1982; David et al., 1994], shear enhance compaction [Zhang et al., 1994], ductile deformation can decrease the pore space and reduce the permeability. Little is known regarding the effect on fluid-transport properties in rocks undergoing ductile deformation by crystal plastic or diffusion flow mechanisms [see Fischer and Paterson, 1989]. When rocks are deformed in the tri-axial configuration at elevated temperatures and large effective pressures, permeability and porosity tend to be reduced with strain, although the response depends critically on the state of drainage of the pore fluid [Fischer and Paterson, 1989]. In undrained mechanical tests on partially molten peridotite, melt-rich lenses develop with spacing that is related to the permeability of the rock matrix and the viscosity of the melt [Holtzman et al., 2003]. Permeability was not measured directly, but microstructure suggests that the melt rich lenses have a much higher in permeability, but that the lenses evolve and move throughout the aggregate.
[69] We can make some simplified first order estimates of the depth of the brittle/ductile transition in the basaltic crust to constrain the maximum depth at which hydrothermal fluids circulate. Even with this first order approach it requires large extrapolations in strain rate of our laboratory data to the mechanical behavior in natural situations. Here we suggest a simple rheological model based only on GBF data, fully recognizing limitations the simple model. The friction law of GB and GFB and power law for GFB were used to calculate the strength as a function of depth, assuming a strain rate of 1014s1and two different thermal gradients suggested for the oceanic crust at the axial Ice-landic rift [Foulger, 1995] (Figure 12).
[70] In addition to assuming that the large extrapolation in strain rate is valid, one must also assume constant strain rate throughout the section, and that the entire oceanic crust consists of basalt of the same chemistry, that strength in the localized regime is determined by the stress to cause slip on a optimally oriented fault, that the rocks are effectively drained, and that local heterogeneities in fluid pressure do not exist. Even so, the validity of the extrapolation strongly depends on the accuracy of the determination ofm, n, and Q in the constitutive relations. For GFB sample the error of Q is4 kJ/mol, which corresponds to an error of 200 m in depth. The standard deviation of n 0.6 for GB and GFB causes an error of about 600 m on the depth of the brittle to ductile transition, we obtained similar values to that for Columbia and Maryland diabase given by Mackwell et al. [1998].
[71] With these assumptions we estimate that glass free basalt may deform in the brittle field up to 550 100C at 1014 s1. In Figure 12a, GB rheology is also given for comparison.
[72] If these extrapolations are correct, hydrothermal fluids might circulate, at least transiently, through the oce-anic basaltic crust down to 5 to 7 km depth. Clearly, super-critical fluids might be expected at these depths within the volcanic rift zone (Figure 12). This estimate is coherent with the lower limit of the Icelandic seismogenic zone, which seems to be associated with the isotherm for 650 100C [Fridleifsson and Elders, 2005].
[73] Some geological observations also agree with this model. Several petrological studies based on ophiolite petrology and on characterizations of the oceanic crust sug-gest that high temperature metamorphism (500–700C) in
diabase and gabbros can be linked to hydrothermal circula-tion e.g., Diabase in at Hole IODP 1256D are altered in the amphibolite facies [Wilson et al., 2006]. Gabbros from Hess deep (Site IODP 894) show also alteration at temperatures of 700–750C [Manning et al., 1996]. Sheeted dikes com-plex at Troddos Ophiolite show hydrothermal alteration of 550750C [Gillis, 2002].
[74] It is important to emphasize that, because of the high temperature, large values of effective lithostatic pressure are not likely to persist, and that reductions in permeability owing to mineral crystallization or compaction of the solid matrix. Once again, the physical and chemical state of the pore fluids, whether aqueous or silicate, will be an extremely important parameters, and these will quite probably evolve. Additional tests are needed, particularly experiments where permeability and volumetric strain could be measured Figure 12. (a and b) Differential stress versus depth profile for a typical Iceland crust at the rift axis.
(c) Strain rate of 1014 s1 was used in all calculation. (d) Thermal profile used in calculation [Foulger, 1995].
VIOLAY ET AL.: BRITTLE-DUCTILE TRANSITION OF BASALT B03213 B03213
